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Theorem ancld 308
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)
Hypothesis
Ref Expression
ancld.1 (φ → (ψχ))
Assertion
Ref Expression
ancld (φ → (ψ → (ψ χ)))

Proof of Theorem ancld
StepHypRef Expression
1 idd 21 . 2 (φ → (ψψ))
2 ancld.1 . 2 (φ → (ψχ))
31, 2jcad 291 1 (φ → (ψ → (ψ χ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101
This theorem is referenced by:  mopick2  1965  cgsexg  2566  cgsex2g  2567  cgsex4g  2568  reximdva0m  3213  difsn  3475  preq12b  3515  elres  4573  relssres  4575  fnoprabg  5525  1idprl  6429  1idpru  6430
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